Cohomology-free diffeomorphisms on tori

2014/03/09 by Santos, Nathan M. Dos
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.2074

Abstract

A smooth diffeomorphism f of a smooth closed orientable manifold M is cohomology-free diffeomorphism (c.f) if for each smooth function g on M there exists a smooth function h on M and a constant c such that h-h o f = g. In this article we show that (c.f) diffeomorphisms on tori are conjugate to Diophantine translations. This is part of a conjecture of A. Katok [H, Problem 17].

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